Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(51,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.bb (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.855355656503296000000000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 12x^{14} + 95x^{12} + 552x^{10} + 1969x^{8} + 27048x^{6} + 228095x^{4} + 1411788x^{2} + 5764801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 259.4 | ||
Root | \(-1.64697 + 2.07063i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.259 |
Dual form | 572.2.bb.a.519.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34500 | − | 0.437016i | 0.951057 | − | 0.309017i | ||||
\(3\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(4\) | 1.61803 | − | 1.17557i | 0.809017 | − | 0.587785i | ||||
\(5\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59357 | + | 3.56974i | 0.980276 | + | 1.34923i | 0.936680 | + | 0.350185i | \(0.113881\pi\) |
0.0435957 | + | 0.999049i | \(0.486119\pi\) | |||||||
\(8\) | 1.66251 | − | 2.28825i | 0.587785 | − | 0.809017i | ||||
\(9\) | 0.927051 | + | 2.85317i | 0.309017 | + | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.815716 | + | 3.21475i | −0.245948 | + | 0.969283i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.42908 | + | 1.11418i | −0.951057 | + | 0.309017i | ||||
\(14\) | 5.04837 | + | 3.66786i | 1.34923 | + | 0.980276i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | −1.49874 | − | 0.486971i | −0.363499 | − | 0.118108i | 0.121572 | − | 0.992583i | \(-0.461206\pi\) |
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 2.49376 | + | 3.43237i | 0.587785 | + | 0.809017i | ||||
\(19\) | 5.12416 | − | 7.05280i | 1.17556 | − | 1.61802i | 0.584898 | − | 0.811107i | \(-0.301135\pi\) |
0.590665 | − | 0.806917i | \(-0.298865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.307761 | + | 4.68031i | 0.0656149 | + | 0.997845i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | −4.12519 | + | 2.99713i | −0.809017 | + | 0.587785i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.39296 | + | 2.72704i | 1.58612 | + | 0.515362i | ||||
\(29\) | −0.665151 | − | 0.915502i | −0.123515 | − | 0.170004i | 0.742781 | − | 0.669534i | \(-0.233506\pi\) |
−0.866297 | + | 0.499530i | \(0.833506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07286 | − | 9.45728i | −0.551901 | − | 1.69858i | −0.703990 | − | 0.710210i | \(-0.748600\pi\) |
0.152088 | − | 0.988367i | \(-0.451400\pi\) | |||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.22862 | −0.382205 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | + | 3.52671i | 0.809017 | + | 0.587785i | ||||
\(37\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(38\) | 3.80979 | − | 11.7253i | 0.618030 | − | 1.90210i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 2.45931 | + | 6.16050i | 0.370755 | + | 0.928731i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0679 | + | 8.04129i | 1.61442 | + | 1.17294i | 0.846489 | + | 0.532406i | \(0.178712\pi\) |
0.767927 | + | 0.640537i | \(0.221288\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.85333 | + | 11.8593i | −0.550475 | + | 1.69419i | ||||
\(50\) | −6.72499 | − | 2.18508i | −0.951057 | − | 0.309017i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.23858 | + | 5.83390i | −0.587785 | + | 0.809017i | ||||
\(53\) | −2.11959 | − | 6.52342i | −0.291148 | − | 0.896060i | −0.984488 | − | 0.175450i | \(-0.943862\pi\) |
0.693341 | − | 0.720610i | \(-0.256138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.4803 | 1.66775 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.29472 | − | 0.940666i | −0.170004 | − | 0.123515i | ||||
\(59\) | 9.33956 | − | 6.78558i | 1.21591 | − | 0.883408i | 0.220153 | − | 0.975465i | \(-0.429344\pi\) |
0.995754 | + | 0.0920575i | \(0.0293443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4508 | − | 4.69537i | −1.85024 | − | 0.601180i | −0.996795 | − | 0.0799995i | \(-0.974508\pi\) |
−0.853447 | − | 0.521180i | \(-0.825492\pi\) | |||||||
\(62\) | −8.26596 | − | 11.3771i | −1.04978 | − | 1.44490i | ||||
\(63\) | −7.78070 | + | 10.7092i | −0.980276 | + | 1.34923i | ||||
\(64\) | −2.47214 | − | 7.60845i | −0.309017 | − | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.09902 | −0.622944 | −0.311472 | − | 0.950255i | \(-0.600822\pi\) | ||||
−0.311472 | + | 0.950255i | \(0.600822\pi\) | |||||||
\(68\) | −2.99749 | + | 0.973943i | −0.363499 | + | 0.118108i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.53887 | + | 10.8915i | −0.419987 | + | 1.29259i | 0.487726 | + | 0.872997i | \(0.337826\pi\) |
−0.907713 | + | 0.419591i | \(0.862174\pi\) | |||||||
\(72\) | 8.06998 | + | 2.62210i | 0.951057 | + | 0.309017i | ||||
\(73\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 17.4355i | − | 1.99999i | ||||||
\(77\) | −13.5914 | + | 5.42577i | −1.54889 | + | 0.618324i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.934438 | + | 0.303617i | 0.102568 | + | 0.0333263i | 0.359851 | − | 0.933010i | \(-0.382827\pi\) |
−0.257283 | + | 0.966336i | \(0.582827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | + | 7.21110i | 0.639602 | + | 0.768706i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8709 | − | 9.35124i | −1.34923 | − | 0.980276i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.4004 | + | 5.97867i | 1.89786 | + | 0.616652i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(98\) | 17.6347i | 1.78137i | ||||||||
\(99\) | −9.92843 | + | 0.652860i | −0.997845 | + | 0.0656149i | ||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 16.9017 | − | 5.49169i | 1.68178 | − | 0.546444i | 0.696526 | − | 0.717532i | \(-0.254728\pi\) |
0.985256 | + | 0.171087i | \(0.0547281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(104\) | −3.15137 | + | 9.69891i | −0.309017 | + | 0.951057i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.70167 | − | 7.84768i | −0.553796 | − | 0.762234i | ||||
\(107\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.7859 | − | 5.45408i | 1.58612 | − | 0.515362i | ||||
\(113\) | 10.5484 | + | 7.66384i | 0.992307 | + | 0.720954i | 0.960425 | − | 0.278538i | \(-0.0898498\pi\) |
0.0318823 | + | 0.999492i | \(0.489850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.15247 | − | 0.699381i | −0.199852 | − | 0.0649359i | ||||
\(117\) | −6.35787 | − | 8.75086i | −0.587785 | − | 0.809017i | ||||
\(118\) | 9.59627 | − | 13.2081i | 0.883408 | − | 1.21591i | ||||
\(119\) | −2.14873 | − | 6.61312i | −0.196974 | − | 0.606224i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.66922 | − | 5.24464i | −0.879020 | − | 0.476786i | ||||
\(122\) | −21.4883 | −1.94546 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.0897 | − | 11.6898i | −1.44490 | − | 1.04978i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.78492 | + | 17.8042i | −0.515362 | + | 1.58612i | ||||
\(127\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(128\) | −6.65003 | − | 9.15298i | −0.587785 | − | 0.809017i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 38.4665 | 3.33547 | ||||||||
\(134\) | −6.85817 | + | 2.22835i | −0.592455 | + | 0.192500i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.60598 | + | 2.61990i | −0.309211 | + | 0.224655i | ||||
\(137\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.1956i | 1.35911i | ||||||||
\(143\) | −0.784640 | − | 11.9325i | −0.0656149 | − | 0.997845i | ||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.67081 | + | 13.3107i | −0.786999 | + | 1.08321i | 0.207476 | + | 0.978240i | \(0.433475\pi\) |
−0.994475 | + | 0.104971i | \(0.966525\pi\) | |||||||
\(152\) | −7.61959 | − | 23.4507i | −0.618030 | − | 1.90210i | ||||
\(153\) | − | 4.72762i | − | 0.382205i | ||||||
\(154\) | −15.9093 | + | 13.2373i | −1.28201 | + | 1.06669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.451627 | − | 0.328126i | −0.0360438 | − | 0.0261873i | 0.569618 | − | 0.821910i | \(-0.307091\pi\) |
−0.605661 | + | 0.795723i | \(0.707091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.48128 | + | 10.2971i | −0.587785 | + | 0.809017i | ||||
\(163\) | −2.85019 | − | 8.77199i | −0.223244 | − | 0.687075i | −0.998465 | − | 0.0553849i | \(-0.982361\pi\) |
0.775221 | − | 0.631690i | \(-0.217639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.38950 | 0.107846 | ||||||||
\(167\) | −17.5166 | + | 5.69148i | −1.35547 | + | 0.440420i | −0.894529 | − | 0.447010i | \(-0.852489\pi\) |
−0.460944 | + | 0.887429i | \(0.652489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | − | 7.64121i | 0.809017 | − | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.8732 | + | 8.08179i | 1.90210 | + | 0.618030i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.47716 | + | 11.6678i | −0.644506 | + | 0.887087i | −0.998846 | − | 0.0480298i | \(-0.984706\pi\) |
0.354339 | + | 0.935117i | \(0.384706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 22.0622i | − | 1.66775i | ||||||
\(176\) | 11.2213 | + | 7.07682i | 0.845841 | + | 0.533435i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.88573 | + | 24.2698i | −0.586142 | + | 1.80396i | 0.00849335 | + | 0.999964i | \(0.497296\pi\) |
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | −21.3979 | − | 6.95261i | −1.58612 | − | 0.515362i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.78804 | − | 4.42085i | 0.203882 | − | 0.323285i | ||||
\(188\) | 27.3613 | 1.99553 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.70665 | + | 23.7186i | 0.550475 | + | 1.69419i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | −13.0684 | + | 5.21698i | −0.928731 | + | 0.370755i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −13.4500 | + | 4.37016i | −0.951057 | + | 0.309017i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.3328 | − | 14.7726i | 1.43061 | − | 1.03940i | ||||
\(203\) | 1.54299 | − | 4.74883i | 0.108297 | − | 0.333303i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.4222i | 1.00000i | ||||||||
\(209\) | 18.4931 | + | 22.2260i | 1.27920 | + | 1.53740i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(212\) | −11.0983 | − | 8.06339i | −0.762234 | − | 0.553796i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.7904 | − | 35.4974i | 1.75076 | − | 2.40972i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.68189 | 0.382205 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6260 | + | 14.9856i | 1.38122 | + | 1.00351i | 0.996765 | + | 0.0803677i | \(0.0256095\pi\) |
0.384452 | + | 0.923145i | \(0.374391\pi\) | |||||||
\(224\) | 20.1935 | − | 14.6714i | 1.34923 | − | 0.980276i | ||||
\(225\) | 4.63525 | − | 14.2658i | 0.309017 | − | 0.951057i | ||||
\(226\) | 17.5368 | + | 5.69804i | 1.16653 | + | 0.379028i | ||||
\(227\) | 8.24474 | + | 11.3479i | 0.547223 | + | 0.753187i | 0.989632 | − | 0.143626i | \(-0.0458762\pi\) |
−0.442409 | + | 0.896813i | \(0.645876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.20071 | −0.210137 | ||||||||
\(233\) | −16.6033 | + | 5.39475i | −1.08772 | + | 0.353422i | −0.797365 | − | 0.603497i | \(-0.793773\pi\) |
−0.290355 | + | 0.956919i | \(0.593773\pi\) | |||||||
\(234\) | −12.3756 | − | 8.99139i | −0.809017 | − | 0.587785i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.13479 | − | 21.9586i | 0.464435 | − | 1.42938i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.78008 | − | 7.95559i | −0.374667 | − | 0.515685i | ||||
\(239\) | −13.4319 | + | 18.4874i | −0.868836 | + | 1.19585i | 0.110554 | + | 0.993870i | \(0.464738\pi\) |
−0.979390 | + | 0.201980i | \(0.935262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −15.2971 | − | 2.82843i | −0.983332 | − | 0.181818i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28.9017 | + | 9.39073i | −1.85024 | + | 0.601180i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.71310 | + | 29.8939i | −0.618030 | + | 1.90210i | ||||
\(248\) | −26.7492 | − | 8.69135i | −1.69858 | − | 0.551901i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(252\) | 26.4746i | 1.66775i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | 25.6935 | − | 18.6674i | 1.60272 | − | 1.16444i | 0.720670 | − | 0.693279i | \(-0.243834\pi\) |
0.882046 | − | 0.471163i | \(-0.156166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.99545 | − | 2.74651i | 0.123515 | − | 0.170004i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 51.7373 | − | 16.8105i | 3.17222 | − | 1.03072i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.25039 | + | 5.99426i | −0.503973 | + | 0.366158i | ||||
\(269\) | 9.30979 | − | 28.6526i | 0.567628 | − | 1.74698i | −0.0923827 | − | 0.995724i | \(-0.529448\pi\) |
0.660011 | − | 0.751256i | \(-0.270552\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.05761 | − | 4.20844i | −0.185736 | − | 0.255644i | 0.705987 | − | 0.708225i | \(-0.250504\pi\) |
−0.891724 | + | 0.452580i | \(0.850504\pi\) | |||||||
\(272\) | −3.70510 | + | 5.09963i | −0.224655 | + | 0.309211i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.7475 | − | 10.6066i | 0.768706 | − | 0.639602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.8967 | + | 7.43958i | −1.37573 | + | 0.447001i | −0.901263 | − | 0.433273i | \(-0.857359\pi\) |
−0.474465 | + | 0.880274i | \(0.657359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.1345 | − | 17.5348i | 1.44490 | − | 1.04978i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(284\) | 7.07775 | + | 21.7831i | 0.419987 | + | 1.29259i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.27003 | − | 15.7063i | −0.370755 | − | 0.928731i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.1400 | − | 5.24419i | 0.951057 | − | 0.309017i | ||||
\(289\) | −11.7442 | − | 8.53266i | −0.690835 | − | 0.501921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.19021 | + | 22.1292i | −0.413750 | + | 1.27339i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.4966 | − | 28.2112i | −1.17556 | − | 1.61802i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.06605 | − | 6.35863i | −0.118108 | − | 0.363499i | ||||
\(307\) | − | 31.6766i | − | 1.80788i | −0.427663 | − | 0.903938i | \(-0.640663\pi\) | ||
0.427663 | − | 0.903938i | \(-0.359337\pi\) | |||||||
\(308\) | −15.6130 | + | 24.7568i | −0.889634 | + | 1.41065i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.68411 | + | 11.3385i | −0.208238 | + | 0.640891i | 0.791327 | + | 0.611393i | \(0.209391\pi\) |
−0.999565 | + | 0.0294975i | \(0.990609\pi\) | |||||||
\(314\) | −0.750834 | − | 0.243961i | −0.0423720 | − | 0.0137675i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.48568 | − | 1.39150i | 0.195161 | − | 0.0779093i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.1143 | + | 8.07503i | −0.618417 | + | 0.449306i | ||||
\(324\) | −5.56231 | + | 17.1190i | −0.309017 | + | 0.951057i | ||||
\(325\) | 17.1454 | + | 5.57088i | 0.951057 | + | 0.309017i | ||||
\(326\) | −7.66700 | − | 10.5527i | −0.424636 | − | 0.584461i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 60.3651i | 3.32803i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.0326 | 1.81564 | 0.907819 | − | 0.419363i | \(-0.137747\pi\) | ||||
0.907819 | + | 0.419363i | \(0.137747\pi\) | |||||||
\(332\) | 1.86888 | − | 0.607234i | 0.102568 | − | 0.0333263i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.0725 | + | 15.3100i | −1.15303 | + | 0.837728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8668 | − | 21.8387i | −0.864318 | − | 1.18963i | −0.980522 | − | 0.196407i | \(-0.937073\pi\) |
0.116204 | − | 0.993225i | \(-0.462927\pi\) | |||||||
\(338\) | 10.8063 | − | 14.8736i | 0.587785 | − | 0.809017i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.9093 | − | 2.16401i | 1.78214 | − | 0.117188i | ||||
\(342\) | 36.9862 | 1.99999 | ||||||||
\(343\) | −22.9532 | + | 7.45794i | −1.23935 | + | 0.402691i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.30273 | + | 19.3978i | −0.338837 | + | 1.04283i | ||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(350\) | −9.64153 | − | 29.6736i | −0.515362 | − | 1.58612i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.1854 | + | 4.61439i | 0.969283 | + | 0.245948i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.27919 | + | 8.64256i | 0.331403 | + | 0.456137i | 0.941906 | − | 0.335877i | \(-0.109033\pi\) |
−0.610503 | + | 0.792014i | \(0.709033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6137 | − | 54.2093i | −0.927035 | − | 2.85312i | ||||
\(362\) | 36.0890i | 1.89680i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −31.8186 | −1.66775 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7896 | − | 24.4853i | 0.923590 | − | 1.27121i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.1189i | 1.92194i | 0.276649 | + | 0.960971i | \(0.410776\pi\) | ||||
−0.276649 | + | 0.960971i | \(0.589224\pi\) | |||||||
\(374\) | 1.81792 | − | 7.16446i | 0.0940025 | − | 0.370465i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 36.8009 | − | 11.9573i | 1.89786 | − | 0.616652i | ||||
\(377\) | 3.30089 | + | 2.39824i | 0.170004 | + | 0.123515i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0298 | − | 33.9462i | 0.566562 | − | 1.74370i | −0.0967022 | − | 0.995313i | \(-0.530829\pi\) |
0.663264 | − | 0.748385i | \(-0.269171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.29360 | + | 19.3697i | 0.321588 | + | 0.989746i | 0.972957 | + | 0.230985i | \(0.0741949\pi\) |
−0.651369 | + | 0.758761i | \(0.725805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.67328 | + | 4.84842i | −0.338349 | + | 0.245825i | −0.743965 | − | 0.668219i | \(-0.767057\pi\) |
0.405616 | + | 0.914044i | \(0.367057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 20.7308 | + | 28.5336i | 1.04707 | + | 1.44116i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.2971 | + | 12.7279i | −0.768706 | + | 0.639602i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.1803 | + | 11.7557i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.0742 | + | 29.0061i | 1.04978 | + | 1.44490i | ||||
\(404\) | 20.8916 | − | 28.7549i | 1.03940 | − | 1.43061i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 7.06147i | − | 0.350455i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 48.4455 | + | 15.7409i | 2.38385 | + | 0.774559i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.30273 | + | 19.3978i | 0.309017 | + | 0.951057i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.5863 | + | 21.8121i | 1.69167 | + | 1.06686i | ||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.6827 | + | 39.0332i | −0.616652 | + | 1.89786i | ||||
\(424\) | −18.4510 | − | 5.99510i | −0.896060 | − | 0.291148i | ||||
\(425\) | 4.63137 | + | 6.37454i | 0.224655 | + | 0.309211i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.7180 | − | 63.7635i | −1.00262 | − | 3.08573i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.5191 | + | 12.5156i | −1.85540 | + | 0.602857i | −0.859639 | + | 0.510902i | \(0.829311\pi\) |
−0.995763 | + | 0.0919547i | \(0.970689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6935 | − | 10.6754i | 0.706124 | − | 0.513029i | −0.175797 | − | 0.984426i | \(-0.556250\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(434\) | 19.1750 | − | 59.0147i | 0.920431 | − | 2.83279i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.4089 | −1.78137 | ||||||||
\(442\) | 7.64213 | − | 2.48308i | 0.363499 | − | 0.118108i | ||||
\(443\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 34.2908 | + | 11.1418i | 1.62372 | + | 0.527578i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7485 | − | 28.5579i | 0.980276 | − | 1.34923i | ||||
\(449\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(450\) | − | 21.2132i | − | 1.00000i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 26.0770 | 1.22656 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.0484 | + | 11.6598i | 0.753187 | + | 0.547223i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7450 | 0.685260 | 0.342630 | − | 0.939470i | \(-0.388682\pi\) | ||||
0.342630 | + | 0.939470i | \(0.388682\pi\) | |||||||
\(464\) | −4.30495 | + | 1.39876i | −0.199852 | + | 0.0649359i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.9738 | + | 14.5118i | −0.925270 | + | 0.672248i | ||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | −20.5745 | − | 6.68506i | −0.951057 | − | 0.309017i | ||||
\(469\) | −13.2246 | − | 18.2022i | −0.610658 | − | 0.840498i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 32.6523i | − | 1.50294i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.4553 | + | 13.4697i | −1.90210 | + | 0.618030i | ||||
\(476\) | −11.2509 | − | 8.17426i | −0.515685 | − | 0.374667i | ||||
\(477\) | 16.6474 | − | 12.0951i | 0.762234 | − | 0.553796i | ||||
\(478\) | −9.98655 | + | 30.7354i | −0.456774 | + | 1.40581i | ||||
\(479\) | −23.0043 | − | 7.47456i | −1.05109 | − | 0.341521i | −0.267997 | − | 0.963420i | \(-0.586362\pi\) |
−0.783098 | + | 0.621899i | \(0.786362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.8106 | + | 2.88083i | −0.991389 | + | 0.130947i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0066 | + | 25.4338i | 1.58630 | + | 1.15252i | 0.908988 | + | 0.416823i | \(0.136856\pi\) |
0.677315 | + | 0.735693i | \(0.263144\pi\) | |||||||
\(488\) | −34.7688 | + | 25.2610i | −1.57391 | + | 1.14351i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.551068 | + | 1.69601i | 0.0248188 | + | 0.0763846i | ||||
\(494\) | 44.4519i | 1.99999i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −39.7759 | −1.78599 | ||||||||
\(497\) | −48.0582 | + | 15.6151i | −2.15571 | + | 0.700431i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.5977 | + | 21.5040i | −1.32497 | + | 0.962650i | −0.325118 | + | 0.945674i | \(0.605404\pi\) |
−0.999856 | + | 0.0169761i | \(0.994596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(504\) | 11.5698 | + | 35.6083i | 0.515362 | + | 1.58612i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.5200 | − | 6.99226i | −0.951057 | − | 0.309017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.3997 | − | 36.3361i | 1.16444 | − | 1.60272i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.8790 | + | 29.0211i | −1.53398 | + | 1.27634i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.4717 | + | 25.7717i | −1.55404 | + | 1.12908i | −0.613351 | + | 0.789810i | \(0.710179\pi\) |
−0.940690 | + | 0.339267i | \(0.889821\pi\) | |||||||
\(522\) | 1.48361 | − | 4.56609i | 0.0649359 | − | 0.199852i | ||||
\(523\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6704i | 0.682615i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.0187 | + | 20.3568i | 1.21591 | + | 0.883408i | ||||
\(532\) | 62.2401 | − | 45.2201i | 2.69845 | − | 1.96054i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.47716 | + | 11.6678i | −0.366158 | + | 0.503973i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 42.6062i | − | 1.83688i | ||||||
\(539\) | −34.9815 | − | 22.0613i | −1.50676 | − | 0.950248i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(542\) | −5.95163 | − | 4.32411i | −0.255644 | − | 0.185736i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.75473 | + | 8.47818i | −0.118108 | + | 0.363499i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 45.5836i | − | 1.94546i | ||||||
\(550\) | 12.5102 | − | 19.8367i | 0.533435 | − | 0.845841i | ||||
\(551\) | −9.86519 | −0.420271 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.5447 | + | 20.0124i | −1.17026 | + | 0.850247i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(558\) | 24.7979 | − | 34.1314i | 1.04978 | − | 1.44490i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.7683 | − | 12.2717i | −1.58612 | − | 0.515362i | ||||
\(568\) | 19.0391 | + | 26.2051i | 0.798863 | + | 1.09954i | ||||
\(569\) | −16.0035 | + | 22.0269i | −0.670900 | + | 0.923415i | −0.999780 | − | 0.0209564i | \(-0.993329\pi\) |
0.328880 | + | 0.944372i | \(0.393329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −15.2971 | − | 18.3848i | −0.639602 | − | 0.768706i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.4164 | − | 14.1068i | 0.809017 | − | 0.587785i | ||||
\(577\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(578\) | −19.5248 | − | 6.34400i | −0.812125 | − | 0.263876i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.33969 | + | 4.12315i | 0.0555798 | + | 0.171057i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.7001 | − | 1.49268i | 0.940143 | − | 0.0618206i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.1267 | − | 26.9742i | 1.53238 | − | 1.11334i | 0.577490 | − | 0.816398i | \(-0.304032\pi\) |
0.954895 | − | 0.296945i | \(-0.0959677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −82.4461 | − | 26.7884i | −3.39713 | − | 1.10380i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7157 | − | 17.5017i | −0.518686 | − | 0.713910i | 0.466668 | − | 0.884433i | \(-0.345454\pi\) |
−0.985354 | + | 0.170523i | \(0.945454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.72705 | − | 14.5484i | −0.192500 | − | 0.592455i | ||||
\(604\) | 32.9059i | 1.33892i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(608\) | −39.8967 | − | 28.9866i | −1.61802 | − | 1.17556i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.9121 | − | 15.2427i | −1.89786 | − | 0.616652i | ||||
\(612\) | −5.55765 | − | 7.64945i | −0.224655 | − | 0.309211i | ||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | −13.8432 | − | 42.6049i | −0.558664 | − | 1.71939i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.1804 | + | 40.1209i | −0.410178 | + | 1.61652i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.8096 | − | 26.7438i | −1.47950 | − | 1.07492i | −0.977716 | − | 0.209932i | \(-0.932676\pi\) |
−0.501788 | − | 0.864991i | \(-0.667324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 16.8603i | 0.673873i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.11648 | −0.0445525 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2799 | − | 13.2811i | 0.727709 | − | 0.528712i | −0.161129 | − | 0.986933i | \(-0.551513\pi\) |
0.888838 | + | 0.458222i | \(0.151513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 44.9599i | − | 1.78137i | ||||||
\(638\) | 4.08012 | − | 3.39487i | 0.161534 | − | 0.134404i | ||||
\(639\) | −34.3561 | −1.35911 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.6216 | + | 19.3417i | 1.05149 | + | 0.763953i | 0.972495 | − | 0.232922i | \(-0.0748288\pi\) |
0.0789953 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.58924 | − | 4.89119i | 0.0626737 | − | 0.192890i | −0.914817 | − | 0.403869i | \(-0.867665\pi\) |
0.977491 | + | 0.210979i | \(0.0676652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.4198 | + | 15.7180i | −0.449306 | + | 0.618417i | ||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 25.4558i | 1.00000i | ||||||||
\(649\) | 14.1955 | + | 35.5594i | 0.557223 | + | 1.39583i | ||||
\(650\) | 25.4951 | 1.00000 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.9238 | − | 10.8428i | −0.584461 | − | 0.424636i | ||||
\(653\) | −40.8386 | + | 29.6710i | −1.59814 | + | 1.16112i | −0.707177 | + | 0.707037i | \(0.750031\pi\) |
−0.890962 | + | 0.454079i | \(0.849969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.3805 | + | 81.1908i | 1.02842 | + | 3.16515i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 44.4288 | − | 14.4358i | 1.72677 | − | 0.561063i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.24826 | − | 1.63346i | 0.0872494 | − | 0.0633904i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −21.6517 | + | 29.8010i | −0.837728 | + | 1.15303i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8822 | − | 42.6258i | 1.03778 | − | 1.64555i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.1304 | − | 10.4398i | 1.23854 | − | 0.402425i | 0.384736 | − | 0.923026i | \(-0.374292\pi\) |
0.853800 | + | 0.520602i | \(0.174292\pi\) | |||||||
\(674\) | −30.8846 | − | 22.4390i | −1.18963 | − | 0.864318i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.03444 | − | 24.7275i | 0.309017 | − | 0.951057i | ||||
\(677\) | −39.0476 | − | 12.6873i | −1.50072 | − | 0.487614i | −0.560493 | − | 0.828159i | \(-0.689388\pi\) |
−0.940228 | + | 0.340545i | \(0.889388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 43.3173 | − | 17.2925i | 1.65870 | − | 0.662164i | ||||
\(683\) | 51.3202 | 1.96371 | 0.981857 | − | 0.189625i | \(-0.0607272\pi\) | ||||
0.981857 | + | 0.189625i | \(0.0607272\pi\) | |||||||
\(684\) | 49.7464 | − | 16.1636i | 1.90210 | − | 0.618030i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −27.6127 | + | 20.0618i | −1.05426 | + | 0.765963i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5365 | + | 20.0077i | 0.553796 | + | 0.762234i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.22949 | + | 25.3278i | 0.313065 | + | 0.963514i | 0.976544 | + | 0.215319i | \(0.0690792\pi\) |
−0.663479 | + | 0.748195i | \(0.730921\pi\) | |||||||
\(692\) | 28.8444i | 1.09650i | ||||||||
\(693\) | −28.0806 | − | 33.7487i | −1.06669 | − | 1.28201i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25.9357 | − | 35.6974i | −0.980276 | − | 1.34923i | ||||
\(701\) | −18.1128 | + | 24.9302i | −0.684112 | + | 0.941599i | −0.999974 | − | 0.00720582i | \(-0.997706\pi\) |
0.315862 | + | 0.948805i | \(0.397706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 26.4758 | − | 1.74096i | 0.997845 | − | 0.0656149i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 63.4396 | + | 46.0916i | 2.38589 | + | 1.73345i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.2224 | + | 8.88011i | 0.456137 | + | 0.331403i | ||||
\(719\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −47.3807 | − | 65.2139i | −1.76333 | − | 2.42701i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.7715 | + | 48.5396i | 0.586142 | + | 1.80396i | ||||
\(725\) | 5.65811i | 0.210137i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | −42.7959 | + | 13.9052i | −1.58612 | + | 0.515362i | ||||
\(729\) | −21.8435 | − | 15.8702i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.15935 | − | 16.3921i | 0.153212 | − | 0.603809i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2316 | + | 6.57363i | −0.744230 | + | 0.241815i | −0.656497 | − | 0.754329i | \(-0.727962\pi\) |
−0.0877335 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.2265 | − | 40.7070i | 0.485560 | − | 1.49440i | ||||
\(743\) | 48.8120 | + | 15.8600i | 1.79074 | + | 0.581846i | 0.999558 | − | 0.0297385i | \(-0.00946745\pi\) |
0.791179 | + | 0.611584i | \(0.209467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.2215 | + | 49.9248i | 0.593913 | + | 1.82788i | ||||
\(747\) | 2.94758i | 0.107846i | ||||||||
\(748\) | −0.685883 | − | 10.4306i | −0.0250784 | − | 0.381382i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(752\) | 44.2715 | − | 32.1652i | 1.61442 | − | 1.17294i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.48775 | + | 1.78308i | 0.199852 | + | 0.0649359i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.46903 | + | 29.1427i | 0.344158 | + | 1.05921i | 0.962033 | + | 0.272932i | \(0.0879936\pi\) |
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | − | 50.4777i | − | 1.83343i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.9297 | + | 23.3018i | 0.611697 | + | 0.841928i | ||||
\(767\) | −24.4658 | + | 33.6742i | −0.883408 | + | 1.21591i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.3643 | + | 47.2864i | −0.551901 | + | 1.69858i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.85670 | + | 9.43744i | −0.245825 | + | 0.338349i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.1268 | − | 20.2610i | −1.14959 | − | 0.724995i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 40.3526 | + | 29.3178i | 1.44116 | + | 1.04707i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.34500 | + | 0.437016i | 0.0479440 | + | 0.0155779i | 0.332891 | − | 0.942965i | \(-0.391976\pi\) |
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.5316i | 2.04559i | ||||||||
\(792\) | −15.0122 | + | 23.8041i | −0.533435 | + | 0.845841i | ||||
\(793\) | 54.7846 | 1.94546 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.6902 | + | 39.0564i | −0.449510 | + | 1.38345i | 0.427951 | + | 0.903802i | \(0.359236\pi\) |
−0.877461 | + | 0.479648i | \(0.840764\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6720 | − | 17.4416i | −0.448305 | − | 0.617039i | ||||
\(800\) | −16.6251 | + | 22.8825i | −0.587785 | + | 0.809017i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 41.0208 | + | 29.8034i | 1.44490 | + | 1.04978i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.5329 | − | 47.8052i | 0.546444 | − | 1.68178i | ||||
\(809\) | 34.2908 | + | 11.1418i | 1.20560 | + | 0.391724i | 0.841819 | − | 0.539760i | \(-0.181485\pi\) |
0.363783 | + | 0.931484i | \(0.381485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.81878 | + | 8.00886i | −0.204325 | + | 0.281229i | −0.898866 | − | 0.438224i | \(-0.855608\pi\) |
0.694541 | + | 0.719453i | \(0.255608\pi\) | |||||||
\(812\) | −3.08598 | − | 9.49766i | −0.108297 | − | 0.333303i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.7487 | − | 45.3919i | 0.515362 | − | 1.58612i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 72.0381 | 2.50653 | ||||||||
\(827\) | −12.1050 | + | 3.93314i | −0.420931 | + | 0.136769i | −0.511821 | − | 0.859092i | \(-0.671029\pi\) |
0.0908898 | + | 0.995861i | \(0.471029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.4458 | − | 33.0183i | 1.57840 | − | 1.14677i | 0.659897 | − | 0.751356i | \(-0.270600\pi\) |
0.918501 | − | 0.395418i | \(-0.129400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.9543 | + | 23.3356i | 0.587785 | + | 0.809017i | ||||
\(833\) | 11.5503 | − | 15.8976i | 0.400194 | − | 0.550820i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 56.0507 | + | 14.2224i | 1.93855 | + | 0.491892i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.2237 | + | 9.60758i | 0.456533 | + | 0.331691i | 0.792170 | − | 0.610301i | \(-0.208951\pi\) |
−0.335637 | + | 0.941991i | \(0.608951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.56578 | − | 26.3627i | 0.295372 | − | 0.909060i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 58.0421i | 1.99553i | ||||||||
\(847\) | −6.35575 | − | 48.1189i | −0.218386 | − | 1.65339i | ||||
\(848\) | −27.4365 | −0.942173 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.01496 | + | 6.54975i | 0.309211 | + | 0.224655i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(854\) | −55.7313 | − | 76.7076i | −1.90709 | − | 2.62488i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.31626i | − | 0.284078i | −0.989861 | − | 0.142039i | \(-0.954634\pi\) | ||
0.989861 | − | 0.142039i | \(-0.0453659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.3386 | + | 33.6670i | −1.57830 | + | 1.14670i | ||||
\(863\) | 11.0298 | − | 33.9462i | 0.375458 | − | 1.15554i | −0.567711 | − | 0.823228i | \(-0.692171\pi\) |
0.943169 | − | 0.332314i | \(-0.107829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.0974 | − | 20.7797i | 0.513029 | − | 0.706124i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 87.7543i | − | 2.97858i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.4850 | − | 5.68121i | 0.592455 | − | 0.192500i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.2349 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(882\) | −50.3148 | + | 16.3483i | −1.69419 | + | 0.550475i | ||||
\(883\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(884\) | 9.19349 | − | 6.67946i | 0.309211 | − | 0.224655i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.0669 | − | 27.7223i | −0.370755 | − | 0.928731i | ||||
\(892\) | 50.9902 | 1.70728 | ||||||||
\(893\) | 113.427 | − | 36.8547i | 3.79570 | − | 1.23330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.4265 | − | 47.4777i | 0.515362 | − | 1.58612i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.61424 | + | 9.10372i | −0.220597 | + | 0.303626i | ||||
\(900\) | −9.27051 | − | 28.5317i | −0.309017 | − | 0.951057i | ||||
\(901\) | 10.8091i | 0.360104i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.0735 | − | 11.3961i | 1.16653 | − | 0.379028i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(908\) | 26.6805 | + | 8.66903i | 0.885425 | + | 0.287692i | ||||
\(909\) | 31.3375 | + | 43.1323i | 1.03940 | + | 1.43061i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.73829 | + | 2.75632i | −0.0575289 | + | 0.0912208i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 41.2909i | − | 1.35911i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.8320 | − | 6.44382i | 0.651721 | − | 0.211757i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.17886 | + | 3.76266i | −0.170004 | + | 0.123515i | ||||
\(929\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 63.8964 | + | 87.9458i | 2.09412 | + | 2.88231i | ||||
\(932\) | −20.5228 | + | 28.2473i | −0.672248 | + | 0.925270i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −30.5941 | −1.00000 | ||||||||
\(937\) | 7.99343 | − | 2.59722i | 0.261134 | − | 0.0848475i | −0.175524 | − | 0.984475i | \(-0.556162\pi\) |
0.436658 | + | 0.899628i | \(0.356162\pi\) | |||||||
\(938\) | −25.7418 | − | 18.7025i | −0.840498 | − | 0.610658i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −14.2696 | − | 43.9172i | −0.464435 | − | 1.42938i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.8238 | 0.806664 | 0.403332 | − | 0.915054i | \(-0.367852\pi\) | ||||
0.403332 | + | 0.915054i | \(0.367852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −49.8708 | + | 36.2333i | −1.61802 | + | 1.17556i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.7047 | − | 6.07753i | −0.606224 | − | 0.196974i | ||||
\(953\) | 33.9086 | + | 46.6712i | 1.09841 | + | 1.51183i | 0.837477 | + | 0.546472i | \(0.184030\pi\) |
0.260931 | + | 0.965357i | \(0.415970\pi\) | |||||||
\(954\) | 17.1050 | − | 23.5430i | 0.553796 | − | 0.762234i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 45.7033i | 1.47815i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.2072 | −1.10519 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −54.9181 | + | 39.9004i | −1.77155 | + | 1.28711i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 26.8701i | − | 0.864083i | −0.901854 | − | 0.432041i | \(-0.857793\pi\) | ||
0.901854 | − | 0.432041i | \(-0.142207\pi\) | |||||||
\(968\) | −28.0762 | + | 13.4063i | −0.902402 | + | 0.430894i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 58.1988 | + | 18.9099i | 1.86481 | + | 0.605914i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.7245 | + | 49.1705i | −1.14351 | + | 1.57391i | ||||
\(977\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.9295 | − | 28.2839i | 1.24166 | − | 0.902117i | 0.243950 | − | 0.969788i | \(-0.421557\pi\) |
0.997708 | + | 0.0676705i | \(0.0215567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.48237 | + | 2.04031i | 0.0472083 | + | 0.0649766i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.4262 | + | 59.7877i | 0.618030 | + | 1.90210i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −53.4984 | + | 17.3827i | −1.69858 | + | 0.551901i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −57.8141 | + | 42.0044i | −1.83375 | + | 1.33230i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8560 | − | 24.5767i | −0.565506 | − | 0.778352i | 0.426508 | − | 0.904484i | \(-0.359744\pi\) |
−0.992013 | + | 0.126132i | \(0.959744\pi\) | |||||||
\(998\) | −30.4112 | + | 41.8574i | −0.962650 | + | 1.32497i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 572.2.bb.a.259.4 | yes | 16 | |
4.3 | odd | 2 | inner | 572.2.bb.a.259.1 | ✓ | 16 | |
11.2 | odd | 10 | inner | 572.2.bb.a.519.4 | yes | 16 | |
13.12 | even | 2 | inner | 572.2.bb.a.259.1 | ✓ | 16 | |
44.35 | even | 10 | inner | 572.2.bb.a.519.1 | yes | 16 | |
52.51 | odd | 2 | CM | 572.2.bb.a.259.4 | yes | 16 | |
143.90 | odd | 10 | inner | 572.2.bb.a.519.1 | yes | 16 | |
572.519 | even | 10 | inner | 572.2.bb.a.519.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.bb.a.259.1 | ✓ | 16 | 4.3 | odd | 2 | inner | |
572.2.bb.a.259.1 | ✓ | 16 | 13.12 | even | 2 | inner | |
572.2.bb.a.259.4 | yes | 16 | 1.1 | even | 1 | trivial | |
572.2.bb.a.259.4 | yes | 16 | 52.51 | odd | 2 | CM | |
572.2.bb.a.519.1 | yes | 16 | 44.35 | even | 10 | inner | |
572.2.bb.a.519.1 | yes | 16 | 143.90 | odd | 10 | inner | |
572.2.bb.a.519.4 | yes | 16 | 11.2 | odd | 10 | inner | |
572.2.bb.a.519.4 | yes | 16 | 572.519 | even | 10 | inner |